From the clown fish to leopards, skin colour patterns in animals arise from microscopic interactions among coloured cells that obey equations discovered by the mathematician Alan Turing. A multidisciplinary team of biologists, physicists and computer scientists lead by Michel Milinkovitch, professor at the Department of Genetics and Evolution of the UNIGE Faculty of Science, has however demonstrated that some reptiles, such as the ocellated lizard, change the colour of individual skin scales, from black to green and green to black during the whole life of the individual. Milinkovitch then proposed that the network of skin scales form a so-called ‘Cellular Automaton’, an esoteric computational system invented in 1948 by another mathematician: John von Neumann. Cellular automata are abstract lattices of elements in which each element changes its state (here, its colour, green or black) depending on the states of neighbouring elements. Analysis of color change in individual lizards during 4 years of their development, from hatchlings crawling out of the egg to fully mature animals, allowed the researchers to confirm their hypothesis: skin scales are indeed flipping colour depending of the colours of their neighbouring scales. The Geneva team then used computer simulations and demonstrated that the variation of skin thickness (due to the presence of skin scales) impacts on the Turing’s mechanism and makes the cellular automaton emerge. The UNIGE researchers have therefore discovered that a Cellular Automaton as a computational system is not just an abstract concept developed in the genius mind of John von Neumann, but also corresponds to a natural process generated by biological evolution. Stanislav Smirnov, Professor at the UNIGE, who was awarded the Fields Medal in 2010, also closely collaborated with Milinkovitch’s team and he derived a formal mathematical link between Turing’s equations and von Neumann’s automata. For the first time, a biology-driven research allows to link the work of these two mathematical giants.